A Probabilistic Design Method for Fatigue Life of Metallic Component

Abstract

In the present study, a general probabilistic design framework is developed for cyclic fatigue life prediction of metallic hardware using methods that address uncertainty in experimental data and computational model. The methodology involves: (i) fatigue test data conducted on coupons of Ti6Al4V material, (ii) continuum damage mechanics (CDM) based material constitutive models to simulate cyclic fatigue behavior of material, (iii) variance-based global sensitivity analysis, (iv) Bayesian framework for model calibration and uncertainty quantification, and (v) computational life prediction and probabilistic design decision making under uncertainty. The outcomes of computational analyses using the experimental data prove the feasibility of the probabilistic design methods for model calibration in the presence of incomplete and noisy data. Moreover, using probabilistic design methods results in assessment of reliability of fatigue life predicted by computational models.

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth

“…The model output for the case of the stochastic model is represented by d ( θ , ω ), where ω ∈ Ω with Ω the set of possible outcomes. Under the additive noise assumption (see, e.g., [ 63 – 66 ]), the total error is described as ϵ = η + ξ = D − d ( θ , ω ), in which η and ξ indicate data noise and model inadequacy, respectively. Then the likelihood function is the probability density function describing the total error and is written as where p ϵ is a probability distribution.…”

A Predictive Discrete-Continuum Multiscale Model of Plasticity With Quantified Uncertainty

“…Such momentum is because these methods offer general frameworks for predictive modeling while providing means to portray uncertainty. Here, we summarize our Bayesian calibration process, as described in [93] and implemented in [98,99,39,94,32] for predictive modeling of various physical systems. Consider θ to be a vector of model parameters and D to be the observational (training) data.…”

“…The form of the likelihood PDF, π like (D|θ) in (28), represents the statistical distributions of discrepancy between the model output d(θ) and the observational data D. Let p ζ be a probability distribution to the total error due to modeling error, ξ(θ), and data noise, η. Under the additive noise assumption, the total error is described as [32,98]). We assume that the total error is a Gaussian random variable of zero mean, ζ ∼ N (0, Γ −1 noise ), where Γ noise is a covariance matrix [67].…”

Anomalous Features in Internal Cylinder Flow Instabilities subject to Uncertain Rotational Effects

“…The global sensitivity indices introduced in section IV are proper measures to study the importance of each source of randomness on the dynamics of the symmetry-breaking flow instability, which was stochastically computed using PCM in previous section. Variance-based sensitivity analysis is usually performed by employing realizations of random space through Monte Carlo approach 35,36,38,40,45 .…”

“…Uncertainty in modeling procedure and also inaccuracy of the measured data are two main factors in arising epistemic uncertainty. The uncertainty in modeling could be the result of a variety of possibilities including the effects of geometry [30][31][32][33][34] , constitutive laws [35][36][37][38][39][40][41][42][43][44][45][46][47][48] , rheological models [49][50][51] , low-fidelity and reduced-order modeling [52][53][54][55][56][57][58][59][60][61][62][63][64] , and random forcing sources in addition to the random field boundary/initial conditions [65][66][67][68][69][70][71] . In the current work, we seek to fill a gap in the rich literature of investigating flow instabilities inside rotating flow systems by emphasizing on the stochastic modeling of the fluid dynamics and later focusing on the anomalies in the anomalous transport features of such system through statistical and scaling analysis of the response.…”